Inheritance reasoners have traditionally been viewed as argument systems, or algorithms that determine reasonable conclusions by constructing acceptable arguments. While the intended meaning of links in such networks is understood, formal semantic accounts are troublesome, as are semantic accounts of the inference process. We adopt a different perspective, suggesting that links be interpreted as conditional sentences with appropriate truth conditions rather than uninterpreted “reasons.” The conditional logic CT4D is used for this purpose. Furthermore, we characterize inference in our networks in terms of preferred (or minimal) models. In the process, we identify some key differences between our account of inference and those based on the notion of inferential distance, specifically with respect to the stability of reasoning. Key words: nonmonotonic reasoning, inheritance hierarchies, minimal models, conditional logic.